Reference values statistical concepts

International Federation of Clinical Chemistry, Expert Panel on Theory of Reference Values. Approved recommendation on the theory of reference values. Part 1. The concept of reference values. J CUn Chem Clin Biochem 1987 25 337-42 Part 2. Selection of individuals for the production of reference values. J Clin Chem Clin Biochem 1987 25 639-44 Part 3. Preparation of individuals and collection of specimens for the production of reference values. J Clin Chem Clin Biochem 1988 26 593-8 Part 4. Control of analytical variation in the production transfer and application of reference values. Eur J CUn Chem Clin. Biochem 1991 29 531-5 Part 5. Statistical treatment of collected reference values Determination of reference limits. J Clin Chem... 

Statistical Analysis of Results and Performance Characteristics. A common problem with most external quality assurance systems has been the determination of the true value for a control sample. Because the true value is an ideal concept, the data are evaluated against the estimated true value, which may be established from (1) the amount of analyte spiked to the test samples (2) a group of reference laboratories using definitive or reference methods (3) the consensus mean, which is the mean of the results obtained by the participants after exclusion of outlier. It is the responsibility of the coordinators to ensure and demonstrate that the reference values are reliable [6]. 

The degree of data spread around the mean value may be quantified using the concept of standard deviation. O. If the distribution of data points for a certain parameter has a Gaussian or normal distribution, the probabiUty of normally distributed data that is within Fa of the mean value becomes 0.6826 or 68.26%. There is a 68.26% probabiUty of getting a certain parameter within X F a, where X is the mean value. In other words, the standard deviation, O, represents a distance from the mean value, in both positive and negative directions, so that the number of data points between X — a and X -H <7 is 68.26% of the total data points. Detailed descriptions on the statistical analysis using the Gaussian distribution can be found in standard statistics reference books (11). 

Our previous two chapters based on references [1,2] describe how the use of the power concept for a hypothesis test allows us to determine a value for n at which we can state with both a- and / -% certainty that the given data either is or is not consistent with the stated null hypothesis H0. To recap those results briefly, as a lead-in for returning to our main topic [3], we showed that the concept of the power of a statistical hypothesis test allowed us to determine both the a and the j8 probabilities, and that these two known values allowed us to then determine, for every n, what was otherwise a floating quantity, D. 

Elementary concepts of probability and statistics play an important role in this book. Thus, these concepts are an integral part of, e.g., quantum mechanics and statistical mechanics. The probability that some continuous variable x lies between x and x + dx is denoted by P x)dx. Often we refer to P x) as the probability distribution for x (although P(x) strictly speaking is a probability density). The average value or mean value of a variable x, which can take any value between —oo and oo, is defined by... 

Calculation of the contributions of rotation and translation involves the use of quantum statistics, but to obtain a numerical solution the quantum statistics are usually replaced by classical statistics at temperatures above about 10 K below 10 K this classical approximation no longer holds. For this reason the equations presented here fail in the vicinity of 0 K. In agreement with the third-law concept, C° and are zero at 0 K. For a reference element, log A f is zero at 0 K, while for compounds the absolute values of the Gibbs energy function and log become infinite at 0 K, for the choice of the enthalpy reference temperature of 298.15 K. 

The next term, EX, is positive for all the molecular systems of interest for liquids. The name makes reference to the exchange of electrons between A and B. This contribution to AE is sometimes called repulsion (REP) to emphasize the main effect this contribution describes. It is a true quantum mechanical effect, related to the antisymmetry of the electronic wave function of the dimer, or, if one prefers, to the Pauli exclusion principle. Actually these are two ways of expressing the same concept. Particles with a half integer value of the spin, like electrons, are subjected to the Pauli exclusion principle, which states that two particles of this type cannot be described by the same set of values of the characterizing parameters. Such particles are subjected to a special quantum version of the statistics, the Fermi-Dirac statistics, and they are called fermions. Identical fermions have to be described with an antisymmetric wave function the opposite also holds identical particles described by an... 

Assume that c is the true value of some analytical quantity to be determined. For a given measurement series as in Example 2.1. the error is Lf-cl. We already know that x-> E(x) for A->- 00. In the ideal case, where there is no bias, E(x) = c hence, the error will become zero with increasing sample size. Otherwise, the determination has some bias i (.v) - c >0. and the error can only be reduced to the value of this bias. A statistical test for presence of bias is discussed in Section 3.3.2. The concept of precision refers to the scattering of measurements and is given by the (empirical) standard deviation of a measurement series. As long as precision refers to the results of a. single laboratory, it is identified with the concept of repeatability. Precision of results provided by different laboratories is identified with the concept of reproducibility. For a quantification of both concepts, see Chapter 3.4. 

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